There are six numbers written in five different scripts. Can you sort out which is which?
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
What is the sum of all the digits in all the integers from one to
Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Number problems for inquiring primary learners.
Number problems at primary level that may require determination.
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
How many positive integers less than or equal to 4000 can be
written down without using the digits 7, 8 or 9?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. . . .
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Four strategy dice games to consolidate pupils' understanding of rounding.
Can you replace the letters with numbers? Is there only one
solution in each case?
Explore the relationship between simple linear functions and their
How many six digit numbers are there which DO NOT contain a 5?
Who said that adding couldn't be fun?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Follow the clues to find the mystery number.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Think of any three-digit number. Repeat the digits. The 6-digit
number that you end up with is divisible by 91. Is this a
The number 3723(in base 10) is written as 123 in another base. What
is that base?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in
every possible order to give 5 digit numbers. Find the sum of the
There are two forms of counting on Vuvv - Zios count in base 3 and
Zepts count in base 7. One day four of these creatures, two Zios
and two Zepts, sat on the summit of a hill to count the legs of. . . .
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Replace each letter with a digit to make this addition correct.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find the sum of all three-digit numbers each of whose digits is
There are nasty versions of this dice game but we'll start with the nice ones...
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.